Fly-cutting system and method, and related tooling articles

ABSTRACT

Methods of fly-cutting a workpiece are disclosed, and in methods in which the position of a fly-cutting head or its associated cutting element is known as a function of time. Also disclosed are methods of forming features, such as grooves or groove segments, in a workpiece such as a cylindrical roll. The features may be provided according to one or more disclosed patterns. Articles made using tools machined in the manner described are also provided, such as polymeric film or sheeting that exhibit certain beneficial properties.

RELATED APPLICATION

This application is a divisional of U.S. patent application Ser. No.11/834,371, filed Aug. 6, 2007, now pending, which application isgenerally related to the subject matter of U.S. patent application Ser.No. 11/692,257, filed Mar. 28, 2007, now pending, the disclosure ofwhich is incorporated by reference in their entirety herein.

TECHNICAL FIELD

The invention relates to machining systems and methods, and inparticular to fly-cutting systems and methods and related tooling andarticles.

BACKGROUND OF THE INVENTION

One method of machining grooves or other features into a workpiece is touse a rotating fly-cutting head to bring a cutting element into contactwith the workpiece. The head and the workpiece can be moved relative toeach other, which enables the cutting element to cut a long groove intothe workpiece, for example. If the workpiece is a cylindrical roll, afly-cutting head can cut a groove down the length of the outer surfaceof the roll, the roll can be indexed by a distance equal to the spacingor pitch between grooves, and then another groove can be cut down thelength of the roll adjacent to the first groove. In this manner, anentire roll can be provided with longitudinal grooves to form amicroreplication tool, which can in turn be useful for forming polymericsheeting of the type used in displays, or as retroreflective sheeting,for example.

The invention relates to improvements in fly-cutting systems and methodsfor machining workpieces.

SUMMARY OF THE INVENTION

The present invention includes a number of aspects and embodiments,including a method for use in machining a workpiece, comprising thesteps of (a) providing a fly-cutting head adapted for carrying a cuttingelement to machine the workpiece, and for rotation about a central axis;and (b) determining the position of the fly-cutting head with respect tothe central axis as a function of time. The method may also include thesteps of transmitting a position signal that includes informationrelated to the position of the fly-cutting head as a function of time;providing a controller for receiving the position signal that includesinformation related to the position of the fly-cutting head as afunction of time; using information obtained from the transmittedposition signal to create a command signal; and transmitting the commandsignal to a motor that drives the fly-cutting head or to a motor thatcontrols a spindle, to cause a change in the speed of either or both ofthem.

In another respect, the method of the present invention includes thesteps of (a) providing a fly-cutting head adapted for carrying a cuttingelement, and for rotation about a central axis; (b) providing a spindleadapted for carrying the workpiece, and for rotation about a centralaxis; (c) determining the position of the fly-cutting head with respectto the fly-cutter central axis as a function of time; and (d)determining the position of the spindle with respect to the central axisof the spindle as a function of time.

In another embodiment of the method of the present invention, the methodcomprises the steps of (a) providing a fly-cutting head having a cuttingelement; (b) providing the cylindrical workpiece; (c) using thefly-cutting head to form an initial feature in the surface of theworkpiece while the workpiece is rotated around a central axis ofrotation, the initial feature having a major axis extending generallyparallel to the axis of rotation for less than the length of theworkpiece; (d) rotating the workpiece around a central axis of rotation;and (e) using the fly-cutting head to form a subsequent feature in thesurface of the workpiece, the subsequent feature having a major axisextending generally parallel to the axis of rotation, wherein thesubsequent feature is in predetermined location relative to the initialfeature. The subsequent feature may be aligned with and adjoin theinitial feature such that the two features approximate a singlecontinuous feature.

In a further embodiment of the inventive method, the method includes thesteps of (a) forming, beginning near a first end of the workpiece, aninitial portion of each feature or groove; and (b) forming subsequentportions of each feature or groove during successive revolutions of theworkpiece, the subsequent portions being substantially aligned with theinitial portion of each feature or groove, the subsequent portions beingformed progressively closer to a second end of the workpiece. Thismethod can result in the formation of the initial portions of thefeatures or grooves near the first end of the workpiece that arerelatively sharper than the subsequent portions of the features orgrooves formed closer to the second end of the workpiece.

A tool, such as a microreplication tool, made using one or more of themethods described above is also a part of the present invention.Articles, such as a polymeric article, made using such tools are alsowithin the scope of the present invention, as are those polymericarticles in combination with a display such as a television or acomputer display.

Other tools may be provided according to the present invention,including the following: a cylindrical tool comprising a plurality ofgroove segments individually formed around the perimeter of the tool,the groove segments being aligned with other groove segments to formgenerally uniform longitudinally-extending grooves in the tool; acylindrical tool having longitudinally-extending features or groovesextending from a first end toward a second end, wherein portions of thefeatures or grooves nearest the first end are all relatively sharperthan the corresponding portions of the features or grooves near thesecond end; or a cylindrical tool having longitudinally-extendinggrooves extending from a first end toward a second end, wherein the toolis characterized by the absence of a virtual seam along which a sharpgroove is adjacent to a less sharp or dull groove. In certain additionalembodiments, the tool may be a cylindrical tool having groove segmentsformed therein, wherein the groove segments have a beginning and an end,and the groove segments are arranged according to an integer brickpattern, wherein the integer is greater than one.

A further tool provided according to the present invention is acylindrical tool having groove segments formed therein, wherein thegroove segments have a beginning and an end, and successive groovesegments are offset with respect to previous groove segments by a helixangle, as well as a cylindrical tool comprising a plurality of groovesegments, wherein the groove segments are individually formed inpositions relative to each other, and wherein the groove depthdistribution of successive adjacent grooves, measured along a line thatis parallel to any helix angle associated with the groove segments, ismulti-modal.

The present invention includes articles, such as polymeric articles,made using the tools described above, as well as those polymericarticles in combination with a display such as a television or acomputer display.

DESCRIPTION OF THE DRAWINGS

The various aspects of the present invention will be described belowwith reference to the appended Figures, in which:

FIG. 1 is an exploded view of a fly-cutting head according to thepresent invention;

FIG. 2 is an elevational perspective view of a fly-cutting systemaccording to the present invention;

FIG. 3 is an example of a workpiece or roll having groove segments orfeatures formed in the outer surface;

FIGS. 3 a, 5 a, 5 b and 7 a are graphical representations ofgroove-depth distributions determined in accordance with the presentinvention;

FIG. 4 is an elevational perspective view of a fly-cutting head and aworkpiece or roll, in which the head is inclined relative to the roll;

FIGS. 6 through 8 are plan views of exemplary patterns of features orgroove segments formed in a surface of a workpiece;

FIGS. 9 and 10 are elevational perspective views of articles made onworkpieces made according to the present invention;

FIG. 11 is a cross-sectional view of a portion of an idealizedfly-cutting head with a sharp cutting element cutting a groove or groovesegment into a workpiece;

FIG. 12 is a cross-sectional view of a portion of an idealizedfly-cutting head with a less sharp or dull cutting element cutting agroove or groove segment into a workpiece;

FIG. 13 is a sectional cut-away view of a portion of a tool cut inaccordance with the prior art, exhibiting a virtual seam; and

FIG. 14 is a sectional cut-away view of a portion of a tool cut inaccordance with the present invention.

DETAILED DESCRIPTION OF THE INVENTION

In conventional fly-cutting operations, a fly-cutter is positionedrelative to a workpiece, a motor is activated to rotate the head and theassociated cutting element or elements, and the fly-cutting head ismoved relative to the workpiece to cut a groove or other feature intothe workpiece. Fly-cutting, which is a type of milling, is typically adiscontinuous cutting operation, meaning that each cutting element is incontact with the workpiece for a period of time, and then is not incontact with the workpiece for a period of time during which thefly-cutting head is rotating that cutting element through the remainingportion of a circle until it again contacts the workpiece. Although afly-cutting operation is typically discontinuous, the resulting groovesegment or other surface feature formed in a workpiece by the fly-cuttermay be continuous (formed by a succession of individual, but connectedcuts, for example) or discontinuous (formed by disconnected cuts), asdesired. The present invention is described most often in the context ofremoving material from a workpiece by fly-cutting using a cuttingelement, but the present invention also includes within its scope thepractice of peening or otherwise deforming a surface using a modifiedfly-cutting head equipped with peening elements rather than cuttingelements.

As noted above, the feature(s) cut into the workpiece using conventionalfly-cutting may be a groove, formed by the sequential groove segmentsmade by the cutting elements as the head rotates, that extends along thelength of the workpiece. In this arrangement, it is not important toknow where an individual cutting element is relative to the axis ofrotation of the fly-cutting head, because the cutting element simplycontinues to cut material from the workpiece until it is moved away fromthe workpiece, or the motor is stopped. Another example of a similararrangement is when a fly-cutter is used to cut a helical groove intothe surface of a cylindrical workpiece—a process that is said to producethreads, or screw threads, in the workpiece. In that situation as well,the position of any individual cutting element relative to the axis ofrotation of the fly-cutting head is unimportant, because the cuttingelements once positioned relative to the workpiece simply continues tocut that workpiece until they are stopped. In other words, if the pointat which a cutting element first contacts the workpiece is said to be 0degrees (relative to the axis of rotation of the fly-cutter head), it isnot important to know whether a cutting element is located at 5 degrees,165 degrees, or 275 degrees of rotation around the axis of rotation atany point in time.

A feature of the present invention is related to the determination ofthe position of a fly-cutting head as a function of time. Thisinformation is useful for fly-cutting operations in which thefly-cutting head is to be positioned to form a feature, such as a groovesegment, in a workpiece in a specified position relative to theworkpiece or other features, or both. The position determination may beabsolute, meaning that the rotational position of the fly-cutting headis known relative to some initial or reference point, or relative,meaning that the rotational position of the fly-cutting head is knownrelative to some previous position. For example, using the simpleangular position descriptions provided above, the present inventionenables a user or a system to determine that at a first point in time(t₁), the cutting element was at a first angular position (a₁), that ata second point in time (t₂) the cutting element was at a second angularposition (a₂), and so on. If the angular positions are specified as thepositions at which, for example, a cutting element first contacts aworkpiece (at position a₁), and the position at which a cutting elementhas cut a known portion of a groove or other feature into the workpiece(position a₂), then a fly-cutting head equipped with an actuator forchanging the position or the orientation of a cutting element, or both,between position a₁ and position a₂ can be activated to do so. In short,knowing the position of the cutting element as a function of timepermits an operator to specify the position of that cutting element atany point in time, which can enable the system to form predeterminedpatterns, structures, grooves, cuts, designs, or, generically, featuresin a workpiece. This is believed to be an advantage that is notavailable in conventional fly-cutting systems or methods.

The present invention will be described first with reference to afly-cutting head, then a fly-cutting system that includes such afly-cutting head. Finally, various operational features and the resultsof the present invention will be described, particularly in regard toforming tooling or an article made using such a tool.

In the fly-cutting system and method of the present invention, oneembodiment of which is shown in FIG. 1, the fly-cutting head 100includes cutting elements 102 that are retained by or incorporated intoshanks or tool holders 104, which may in turn be affixed to head 100 bycartridges 106. The cutting element may be a diamond, for example, thatis carried by a tool holder 104. Alternatively, a cutting element suchas a diamond may be bonded directly to a fly-cutting head or disc, andused to form features in a workpiece.

The fly-cutting head includes a housing 110 that is normally secured toa base or platform, a motor such as a DC motor that includes a stator(not shown) that is affixed to the housing, and a rotating spindle 112that is supported by an air-bearing 114, which may include ports 108,for example. The fly-cutting head may also include a slip-ring or otherassembly for transmitting signals or power or both between stationaryand rotating portions of the head. The fly-cutting head also includes anencoder, such as rotary encoder that measures the position (or change ofposition) of the rotating spindle relative to the housing 110. One partof the encoder is typically stationary, and is in a fixed positionrelative to (and typically contained within) the housing or the statoror both. A second part of the encoder is typically affixed to a rotatingportion of the fly-cutting head such as spindle 112, and it is adaptedto interact with the stationary part of the encoder to produce a signalthat indicates relative movement between the two parts. For example, therotating part of the encoder may have a series of lines or otherindicia, and the stationary part of the encoder may optically detect thepresence or absence of those lines in order to determine the extent ofthe relative motion between the two parts. The encoder (the stationarypart, typically) then transmits at least one position signal thatincludes information regarding the position of the fly-cutting head,which can be received by a controller and used to create commandsignals. The command signals may be transmitted to the motor associatedwith the fly-cutting head or platform, for example. Command signals maychange the speed of the fly-cutting head, or its location relative tothe workpiece, for example.

Although in the present description reference may be made to a singlecutting element that is carried by a fly-cutting head, multiple cuttingelements may be carried by the fly-cutting head, and the cuttingelements may be identical to or different from each other. The cuttingelements may be single or polycrystalline diamond, carbide, steel, cubicboron nitride (CBN), or of any other suitable material. Suitable diamondcutting tips are available from the K&Y Diamond Company of Quebec,Canada. The geometry of a cutting element such as a diamond, and thedesign of a shank or holder for the cutting element, may be specified tocreate the surface features or effects desired for a workpiece. Thecutting element, which is typically replaceable, may include more thanone cutting tip, or other features, as described for example in U.S.Patent Publication No. 2003/0223830 (Bryan et al.), the contents ofwhich is incorporated herein. Diamond cutting elements can be milled ona sub-micron scale, including for example by ion-milling, to createcutting elements that will form features of almost any desiredconfiguration. Other characteristics of the fly-cutting head can beselected as desired. For example, a larger diameter fly-cutting head canbe used to create grooves that naturally have a flatter bottom, due tothe larger cutting radius, than grooves cut by a smaller diameterfly-cutting head.

A fly-cutting system in accordance with the present invention isillustrated in FIG. 2. For ease of description, a coordinate system maybe designated with regard to the fly-cutting head 100 and a workpiece200. The coordinate system designations are arbitrary, and provided tofacilitate an understanding of the present invention in the context ofthe drawings provided, rather than to limit the scope of the invention.The coordinate system is shown relative to the tip of the cuttingelement, and includes mutually orthogonal X, Y, and Z axes. The X axisis perpendicular to roll 200, and in the illustrated embodiment passesthrough the longitudinal axis of roll 200. The Y axis extendsvertically, as shown in FIG. 2, and in the illustrated embodiment isparallel to or coincident with a tangent to the outer surface of theroll. The Z axis extends horizontally and parallel to the central axisof the roll. The workpiece, in the illustrated embodiment, also has arotational axis C, and the workpiece may be rotated in either directionwith respect to that axis. The fly-cutting head 100 has an axis ofrotation A, which is parallel to the Y axis in FIG. 2. Although theillustrated workpiece is a cylindrical roll, and the designation of aworkpiece and a roll may be used interchangeably in this descriptionwhere the specific shape of the workpiece is unimportant, workpieces ofother shapes and sizes may be used in connection with the presentinvention. If the workpiece is planar (such as a plate or disc) ratherthan cylindrical, then corresponding adaptations in the precedingdesignations of the various axes may be made to facilitate anunderstanding of the invention in that context.

In this embodiment, a cylindrical workpiece 200 is fixedly supported ona spindle 202, and an encoder 226 is positioned and adapted to detectthe position or change in position of the spindle relative to a fixed orinitial point. The workpiece may be a roll 200 made of metal, such asstainless steel, with an outer layer made of a material that is moreeasily tooled, such as brass, aluminum, nickel phosphorus, hard copper,or polymer. For simplicity, the workpiece will often be referred to inthis description as a “roll,” but the workpiece could with suitableadaptations to the system be planar, convex, concave, or of a complex orother shape. Accordingly the term “roll” in this description is intendedto exemplify workpieces of any suitable shape. The workpiece may includea test band 210 at one end, as shown in FIG. 3, on which the fly-cuttinghead can be programmed to cut a test pattern to determine whether thehead and the workpiece are positioned and synchronized appropriatelyrelative to each other. The characteristics of the features formed inthe test band can then be evaluated, and once the operation of thefly-cutting head and the workpiece have been optimized, the actualmachining operation can be performed on a different portion of theworkpiece. Test bands are not required, but they may be useful fordetermining what adjustments may have to be made to cause the actualperformance of the system to match the desired or theoreticalperformance of the system.

The fly-cutting system is preferably controlled by a computer orcontroller 218, which may include or be operatively connected to memoryfor storing one or more applications, secondary storage for non-volatilestorage of information, a function generator for generating waveformdata files that can be output to an actuator or other device, an inputdevice for receiving information or commands, a processor for executingapplications stored in memory or secondary storage or received fromanother source, a display device for outputting a visual display ofinformation, or an output device for outputting information in otherforms such as speakers or a printer, or any combination of two or moreof the foregoing. The controller may exchange data or signals usingcables 220, or a suitable wireless connection. One useful control systemincludes input and output circuitry, and a PMAC control, available fromDelta Tau Data Systems of Chatsworth, Calif. That PMAC control combinesa multi-axis PMAC2 controller with amplifiers to provide motion controlof, for example, the flycutting head and the roll.

The control system of the present invention uses software or firmware orboth that can be designed in a manner known to produce the resultsdescribed herein. Specifically, the software preferably enables anoperator to create waveform data files that represent both themicro-level shape of an individual groove segment or other surfacefeature, and a macro-level pattern (random, pseudo-random, or regular)of groove segments or other features on the workpiece. Those data filesare then communicated to the various control system components tocontrol the performance and preferably the synchronization of thecutting elements relative to the workpiece.

To program and coordinate the movement of the various components,software is typically used to input the desired parameters to createdata files, and a wave generation unit then translates the data filesinto signals that are transmitted to the drive unit(s), actuator(s) andother components as required. For example, the roll speed may be set atfrom approximately 0.001 to approximately 1000 revolutions per minute,and the fly-cutting head speed may be set at from approximately 1000 toapproximately 100,000 revolutions per minute. Fly-cutting head speeds ofapproximately 5000, approximately 10,000, approximately 25,000revolutions, and approximately 40,000 revolutions per minute have beentested, and are generally preferred because higher speeds reduce thetime required to create a finished workpiece, such as a microreplicationtool.

The workpiece—roll 200 in the illustrated embodiment—may be fixedlysupported on a spindle system that is driven by a motor that iscontrolled by and receives command signals from the controller. Thespindle system may include one or more bearings 222, such as air orhydrostatic bearings. For simplicity, bearings 222 are shown at only oneend of the roll in FIG. 2, and are not shown in FIG. 4, although theymay be positioned and supported in any suitable location with respect toa workpiece. The roll may be rotated in either direction by a motor 224or, if the workpiece is not cylindrical or is positioned using adifferent system, positioned in response to instructions provided by thecontroller 218. An exemplary motorized spindle system is available fromProfessional Instruments of Hopkins, Minn., under the designation 4R, orunder the designation 10R (which includes an air bearing), or, forlarger workpieces, an oil hydrostatic spindle system from WhitnonSpindle Division, Whitnon Manufacturing Company, of Farmington, Conn.The spindle system preferably also includes a rotary encoder 226 that isadapted to detect the position of the workpiece to within a desireddegree of accuracy, and to transmit that information to the controllerto enable the controller to synchronize the workpiece and thefly-cutting head in the manner described below.

The fly-cutting head is preferably supported on a fly-cutting table 230,as shown in FIG. 2, which may be referred to as an “x-table.” Thex-table is adapted for movement along at least one of the X, Y, and Zaxes, preferably along both the X and Z, and more preferably along allthree of the X, Y, and Z axes sequentially or preferably simultaneously,to position the fly-cutting head and the cutting element(s) relative tothe workpiece. As is known in the art, the x-table can move in more thanone dimension or direction essentially simultaneously, so that thelocation of the cutting tip can be easily positioned inthree-dimensional space under the control of the controller.

Other conventional machining techniques may useful in connection withthe inventive system and its components. For example, cooling fluid maybe used to control the temperature of the cutting elements, thefly-cutting head, the actuators, or other components. A temperaturecontrol unit may be provided to maintain a substantially constanttemperature of the cooling fluid as it is circulated. The temperaturecontrol unit and a reservoir for cooling fluid can include pumps tocirculate the fluid through or to the various components, and they alsotypically include a refrigeration system to remove heat from the fluidin order to maintain the fluid at a substantially constant temperature.Refrigeration and pump systems to circulate and provide temperaturecontrol of a fluid are known in the art. In certain embodiments, thecooling fluid can also be applied to the workpiece to maintain asubstantially constant surface temperature while the workpiece is beingmachined. The cooling fluid can be an oil product, such as alow-viscosity oil.

Other aspects of the machining process are also known to persons ofskill in the art. For example, a roll may be dry-cut, or cut using oilor another processing aid; high-speed actuators may require cooling;clean, dry air should be used with any air bearings, such as those thatsupport the spindle; and the spindle may be cooled using an oil coolingjacket or the like. Machining systems of this type are typically adaptedto account for a variety of parameters, such as the coordinated speedsof the components and the characteristics of the workpiece material,such as the specific energy for a given volume of metal to be machined,and the thermal stability and properties of the workpiece material.Finally, certain diamond-turning components and techniques of the typedescribed in PCT Publication WO 00/48037, and fly-cutting components andtechniques of the type described in U.S. Patent Publication 2004/0045419A1 (Bryan et al., which is assigned to the assignee of the presentinvention), the contents of both of which are incorporated herein byreference, may also be useful in the context of the present invention.

The position of the workpiece 200 as a function of time is determined,for example in the case of a cylindrical roll by using an encoder 226associated with a spindle on which the roll is fixedly mounted forrotation about a longitudinal axis of rotation. The encoders used forthe fly-cutting head, and for the spindle or other workpiece supportsystem, may be used not only for purposes of measuring speed, as withsome conventional encoders used with fly-cutting systems, but to measureposition. Then encoder can then transmit a position signal indicative ofthe position of the fly-cutting head or the spindle, respectively. Thisassists in synchronizing the positions of the workpiece and the cuttingelement(s) of the fly-cutting head. Specifically, encoders may beprovided to determine the rotational position of a roll, the position ofthe fly-cutting head with respect to its axis of rotation of the head,the position of the fly-cutter head with respect to another axis such asthe Z axis, and the position of an x-table that moves the fly-cutterwith respect to the roll. Accordingly, although the term “determiningthe position” of the fly-cutting head will commonly be used withreference to determining its position during rotation of the head, itmay additionally include determining the position of the fly-cuttinghead with respect to its axial position along or rotational positionaround an axis. In general, the fly-cutting head may be angled withrespect to, or rotated around (or tilted with respect to), any axis.

In one embodiment, this synchronization may be done by providing aposition encoder (such as an angular encoder) associated with the rolland another position encoder associated with the fly-cutting head. Atleast two types of encoders are currently available—incremental andabsolute. Incremental encoders may be less expensive, and if used withan index signal that is indicative of a known position of the roll orthe fly-cutting head, for example, may function effectively as anabsolute encoder. The encoder 226 associated with the roll (or thespindle on which the roll is mounted) should have a resolutionsufficient to detect the position of the roll along its axis of rotationto within a fraction of the desired groove pitch or other dimension ofthe features being machined into the roll. The groove pitch is thedistance from the center of one groove to the center of the nextadjacent groove, or the distance from one peak to the next adjacentpeak, and a corresponding dimension can normally be calculated for othersurface features.

One encoder useful in connection with the flycutting head in certainembodiments of the present invention is available from U.S. DigitalCorp. of Vancouver, Wash., under the designation E5D-100-250-I, and itis positioned on the flycutting head to measure the angular position ofthe head. An encoder that is useful in connection with the workpiece orroll in certain embodiments of the present invention is available fromRenishaw Inc. of Hoffman Estates, Ill., under the designation RenishawSignum RESM, 413 mm diameter, 64,800 line count. The particularencoder(s) selected for an application depends on the desiredresolution, maximum speed of the fly-cutting head or other component,and the maximum signal speed.

Although the features cut into a workpiece by the cutting elements maybe referred to for convenience as a “groove segment” or a “groove,”other surface features may be formed by the cutting elements if desired.The depth of the features cut into a workpiece surface may be in therange of 0 to 150 microns, or preferably 0 to 35 microns, or even morepreferably for creating microreplication tools for optical films, 0 to15 microns. These ranges are not intended to limit the scope of theinvention, but they may represent the scale of features useful forproviding certain optical effects in polymeric sheeting produced usingsuch a tool. For a roll workpiece, the length of any individual featureis influenced by the speed at which the roll rotates around itslongitudinal axis, because it is more difficult to cut a long featureinto a roll moving at a higher speed. If the cutting elements are movingin the opposite direction of the workpiece, longer grooves may generallybe formed more easily than if the cutting elements are moving in thesame direction as the workpiece. The feature can have almost any length,for example if the fly-cutting head of the present invention is used tocreate a feature approximating a thread cut around the perimeter of acylindrical roll. If individual features are desired, their length maybe from about 1 micron to several millimeters, for example, althoughthis range is not intended to limit the scope of the present invention.For thread-cutting, the pitch or spacing between adjacent grooves can beset at from about 1 to about 1000 microns. The features can have anytype of three-dimensional shape such as, for example, symmetrical,asymmetrical, prismatic, and semi-ellipsoidal features. In embodimentsin which the material on the surface of a workpiece is indented orotherwise deformed instead of being removed, the deformation can bechanged by changing the characteristics of the tool carried by the toolholder.

The surface features that are cut into a workpiece in accordance withthe present invention can be controlled on both a macro-scale and on amicro-scale. Surface features or microstructures can include any type,shape, and dimension of structures on, indenting into, or protrudingfrom the surface of an article. For example, microstructures createdusing the actuators and system described in the present specificationcan have a 1000 micron pitch, 100 micron pitch, 1 micron pitch, or evena sub-optical wavelength pitch around 200 nanometers (nm).Alternatively, in other embodiments, the pitch for the microstructurescan be greater than 1000 microns. These dimensions are provided forillustrative purposes only, and features or microstructures made usingthe actuators and system described in the present specification can haveany dimension within the range capable of being tooled using the system.

In cases in which the workpiece is a cylindrical roll that is rotatingaround its longitudinal axis, a flycutting head that is arranged to cuta groove or succession of grooves parallel to that axis may need to bere-oriented so that the resulting groove or succession of grooves isactually parallel. In other words, if the cutting element would cut aparallel groove in the roll when the roll is stationary, then it would(if other parameters were held constant) cut a slightly curved groove inthe roll if the roll is permitted to rotate during the cut. One way tooffset this effect is to angle the cutting head so that the cuttingelement at the end of its cut is farther in the direction of rotation ofthe roll than at the beginning of its cut. Because the cutting elementis in contact with the roll over only a short distance, the result canbe to approximate a parallel cut in the roll surface notwithstanding therotation of the roll. It may be possible to adapt the system in otherways to accomplish the same or a similar objective, for example byenabling the flycutting head to rotate around the central axis of theroll so that it follows the roll as it rotates, although this may beexpensive to implement.

In one useful system and method for machining a workpiece, such as thecylindrical workpiece 200 shown in FIG. 2, the fly-cutting head ispositioned with its axis of rotation A extending parallel to the Y axis,so that grooves or features that extend parallel to the Z axis are cutinto the surface of the workpiece. However, rather than cut an entiregroove down the length of the workpiece, a single groove segment is cutand the workpiece is rotated by an distance (at the outer surface) equalto the desired pitch, or distance, between the desired location ofadjacent grooves. Then a second groove segment is cut, and the workpiecerotated by a second distance equal to the pitch between the desiredlocation of the next adjacent grooves. This process is repeated untilgroove segments have been formed around the perimeter of the workpiece.When the workpiece has been rotated through an entire revolution, thecontroller (because it has received the position signals sent by theencoder associated with the workpiece) can precisely align groovesegments cut into the workpiece during the steps in a successiverevolution with the groove segments cut in steps in a precedingrevolution, to form the equivalent of longitudinally-extending groovesor other desired structures in the outer surface of the workpiece.However, longitudinally-extending grooves are just one of severalpossible features that may be formed in or on a workpiece. In apreferred embodiment described in greater detail below, the rotation ofthe workpiece, the rotation of the fly-cutting head, and thedisplacement of the fly-cutting head in the Z direction are coordinatedand relatively constant, which minimizes wasted time in starting,stopping, or repositioning a component, or waiting for that component toreach a steady operating state.

To form a microreplication tool according to the present invention, aworkpiece such as a cylindrical roll is milled to provide the desiredsurface features. The blank roll may have an outer layer into whichstructures or patterns will be cut. That layer, after it has had arandom or other pattern cut into it, may in turn be coated with one ormore additional layers that protect the pattern, permit accurateformation of a film or its easy release, or perform other usefulfunctions. For example, a thin layer of chrome or a similar material maybe applied to the tool, although a layer of that type may “round over”sharp edges of the tool and therefore be undesirable. Any machineablematerials could be used; for example, the workpiece can be made ofaluminum, nickel, copper, brass, steel, or plastics (such as acrylics).The particular material to be used may depend, for example, upon aparticular desired application such as various films made using themachined workpiece.

FIG. 3 illustrates an idealized workpiece 200, in which individualgroove segments 301 have been formed by fly-cutting during a firstrevolution of the workpiece, after which groove segments 302 have beenformed during a second revolution, after which groove segments 303 havebeen formed during a third revolution, and so on. The groove segmentsformed during the second and subsequent revolutions are aligned with thegroove segments formed during the first revolution, and the result is aset of features approximating longitudinal grooves extending between afirst end and a second end. It is possible to extend the groove segmentsand resulting grooves across the entire length of the workpiece, but itmay be desirable to leave areas on each end of the roll blank, for theformation of test bands or for other purposes.

Although cutting successive groove segments into a workpiece around itsperimeter is believed to have certain advantages when compared toconventional fly-cutting operations, the visual appearance of the areasof the workpiece where successive groove segments overlap may beundesirable. These feature overlaps are shown at 331 (where groovesegments formed during the second revolution overlap with groovesegments formed during the first revolution), 332 (where groove segmentsformed during the third revolution overlap with groove segments formedduring the second revolution), and so on along the length of the roll.If these feature overlaps are visually perceptible on the workpiece,then they are likely to result in corresponding visibly perceptiblestructures on a film or sheeting formed on the workpiece, which can alsobe undesirable. Even if the feature overlaps are not easily visiblyperceptible, it may be desirable to minimize or eliminate them toimprove the optical performance of articles made on the tool. Methods ofminimizing this effect are described in greater detail below.

The position of the fly-cutting head is determined using encoder, asnoted above, and the position of the spindle on which the workpiece iscarried is similarly determined using an encoder shown at 226 in FIG. 2.Because the cutting elements are typically in a fixed position relativeto the fly-cutting head, and the workpiece is typically in a fixedposition relative to the spindle, knowing the position of thefly-cutting head and the spindle essentially enable an operator to knowthe position of the cutting elements and the workpiece. Data from thoseencoders is fed into controller 218, as shown in FIG. 2, which can inturn transmit command signals to the motor that creates the rotarymotion of the fly-cutting head, or the motor that creates the Z-axismotion of the fly-cutting head, or the motor that creates the rotationalmotion of the spindle on which the workpiece is carried, or more thanone of the foregoing, for example. When the relationship between theposition of the fly-cutting head and the workpiece has been determined,the fly-cutting head may be said to be electronically “geared” to theworkpiece, because no actual mechanical gearing between the two piecesexists. When a fly-cutting head is electronically geared to a workpieceaccording to the present invention, the controller can determine when inthe orbit of a cutting element it strikes the workpiece, and where onthe workpiece it strikes. In a further aspect of the invention describedin detail in the copending United States Patent Application firstmentioned and incorporated by reference above, a user can also cause thecontroller to change the position or orientation of a cutting elementrelative to the fly-cutting head if the cutting element is connected toan actuator capable of creating such motion. For example, a user mayprogram the controller to create a groove segment with an essentiallylinear bottom in a workpiece, by activating an actuator that can changethe position of the cutting element thousands of time per second so thatit follows a predetermined cutting path.

When the positions of both the fly-cutting head and the workpiece arecontrolled, in practice one is normally set to rotate at a fixed orpredetermined speed and the other is geared to it (e.g. slowed down orspeeded up) so that the two are in the correct positions relative toeach other. Because the fly-cutting head operates at several thousandrevolutions per minute, it has a considerable amount of energy, inertia,and/or momentum, and it may not be practical to attempt to speed up orslow down the head to match the position of the workpiece. Instead, thefly-cutting head may be programmed to rotate at essentially a fixedrate, and the spindle on which the workpiece or roll is carried may bespeeded up or slowed down so that the cutting element and the workpieceare in the proper positions relative to each other. This system may bereferred to as one in which the fly-cutting head is the “master,” andthe workpiece and its corresponding spindle are “slaved” to it. Thereverse is also possible—slaving the fly-cutting head to theworkpiece—as is a third embodiment in which the rotation of thefly-cutting head, the rotation of the workpiece, and the Z-axis motionof the fly-cutting head are all under synchronized control. Experimentaltesting of the fly-cutting system on the test strip part of theworkpiece is typically helpful in determining whether the head and theworkpiece are appropriately geared together to produce the desiredresults.

Certain relatively simple applications of the present invention aredescribed above, in which grooves or features that are parallel to the Zaxis are formed in or on a workpiece. A variation of the same approachis to form grooves or features in a workpiece at an angle to the Z axis,for example by turning the fly-cutting device 45 degrees relative to itsposition in FIG. 2, as shown in FIG. 4, or turning the head 90 degreesrelative to its position in FIG. 2, or at any other orientation. Toolingmay be created with linear grooves positioned at any angle relative tothe workpiece, or with non-linear features or even features thatintersect each other. Other angular arrangements are also possible,including sets of parallel grooves cut at different angles to produceprisms or other microstructures on the roll or workpiece surface.

Forming grooves or features in a predetermined pattern in a workpiece atan angle to both the Y and Z axes is more complex than forming themparallel to the Z axis. It is more complex because the fly-cutting headis not simply advanced a fixed distance in the Z direction for eachrevolution of the workpiece to form the next groove, as with some of theother embodiments noted above. Instead, the Z-direction travel of thefly-cutting head for each rotation of the workpiece should beanalytically or experimentally determined, so that on successiverotations of the workpiece subsequent groove segments are aligned withearlier groove segments if aligned groove segments are desired. Forexample, if a series of 45 degree groove segments are formed around theperimeter of the roll, each be slightly advanced in the Z directionrelative to the previous segment, then after a complete revolution ofthe roll the groove segments formed during a second revolution would beparallel to the ones formed during the first revolution, but notnecessarily aligned end-to-end with them. One solution to this problemis to calculate the distance by which, after a complete revolution ofthe roll, the groove segments formed during a second revolution shouldbe adjusted in order to make them align end-to-end with the segmentsformed during the first revolution. That distance may then be divided bythe number of groove segments formed during a single revolution, and theresulting fraction added to the pitch between each successive groovesegment so that after a full revolution of the workpiece, the groovesegments formed during the second revolution have effectively precessedby the desired distance with respect to the groove segments formedduring the first revolution. The same process can be used withsuccessive revolutions.

The fly-cutting head may be angled with respect to one or more than oneof the illustrated axes, and may also or instead be rotated around oneor more than one of the axes, so that the cutting elements strike theworkpiece in a predetermined position and orientation. For example, thefly-cutting head could be rotated 90 degrees around the X axis relativeto FIG. 2, so that it is aligned with the Y axis, and then it could berotated around the Y axis at for example a 45 degree angle so that thecutting elements strike the workpiece in a certain manner.

The ability to form grooves at an angle with respect to the longitudinalaxis of a cylindrical workpiece is an advantage relative to conventionalcylindrical tools that include essentially linear grooves parallel orperpendicular to the longitudinal axis of the tool. This is because auser who wishes to use sheeting so that the grooves are at a 45 degreeangle relative to the sides of the sheet would normally need to die-cutthat sheeting at an angle from a larger piece of sheeting having groovesextending longitudinally or laterally. This can result in significantwaste near the sides of the larger piece of sheeting. With the presentinvention, sheeting having grooves extending at a 45 degree angle (orany other selected angle) relative to the sides of the sheeting can bedirectly formed on a tool, with minimal waste along the sides of thesheeting when the sheeting is cut for use.

FIG. 6 illustrates a simplified illustration of the formation of groovesegments or other features in predetermined patterns on a surface of aworkpiece. In this view, groove segments are cut by a cutting element ata certain radius from the axis of rotation of the fly-cutting head, sothe groove segments are relatively narrow and shallow at the point wherethe cutting element enters the workpiece to start forming a groovesegment, wider and deeper at the point where the cutting element is atthe midpoint of the groove segment, and narrow and shallow again at thepoint where the cutting element exits the workpiece at the end of agroove segment. If the cutting element is associated with an actuatorthat can change the position of the cutting element relative to thefly-cutting head, other features with different characteristics can becreated.

In this aspect of the invention, a fly-cutting head forms a groovesegment or feature at a first location 401, the workpiece is rotated bya predetermined amount (1.0 degrees, for example), another groovesegment or feature 402 is formed, the workpiece is rotated by the sameamount, and this operation is repeated until the workpiece had beenrotated 360 degrees—an entire revolution. During the next revolution ofthe workpiece, a groove segment 411, located at a distance Z₁ along theworkpiece toward the far end of the roll, is formed at a point betweenthe features previously cut into the workpiece—for example at arotational position of 0.5 degrees relative to the rotational positionof the groove segment 401. Then the workpiece is rotated (again by 1.0degrees, for example) and a groove segment 412 is formed, and so onaround the workpiece for an entire revolution. The features cut into aworkpiece during a third revolution are aligned with the features cut inthe first revolution; the features cut during a fourth revolutionaligned with those cut in the second revolution, and so on. This mightbe referred to as a “two-brick” pattern, because it is similar to theoffsetting of a second course of bricks laid atop a first course ofbricks by the distance of ½ of the length of an individual brick. Theresult is to decrease the visual significance of feature overlaps if allgrooves ended and began along a single line, because in this embodimentfeatures end and begin along lines 431 and 432, for example. Thecreation of patterned features in a workpiece using a fly-cutting headin the manner described above is one important benefit of the ability todetermine the location of the cutting element as a function of time.

Although the workpiece shown in FIG. 6 has been described for purposessimplicity as groove segments formed in a succession of 1 degreeadvances, followed by a 0.5 degree advance at the end of the firstrevolution, followed by a further succession of 1 degree advances arounda roll, a different process that avoids the necessity of an unequalintermediate step may be preferable. In that process, the desired offsetor advance after a complete revolution (0.5 degrees, in the example) isdivided by the number of groove segments formed during a revolution todetermine an incremental advance to be added to the pitch between eachsuccessive groove segment formed during a first revolution. The resultof that incremental advance for each groove segment, after a completerevolution, is to advance the pattern by a total of 0.5 degrees, in theexample. This process allows the fly-cutting head and the workpiece tobe moved with constant velocities, instead of having a discontinuousshort step or long step at the end of each revolution.

The groove segments or features shown in FIG. 6 can be formed in a rollfollowing a “helix angle” α, so that each successive groove segment isoffset in the Z direction relative to the previous segment. The helixangle may be selected so that after a complete revolution of the roll,the groove segments or features have advanced by the length of onegroove segment. FIG. 6 illustrates what might be referred to as atwo-brick pattern that includes a helix angle. Each successive groovesegment or feature formed during a revolution is offset in the Zdirection by a helix angle alpha (α) relative to the preceding groovesegment or feature. The helix angle is selected so that after one fullrevolution of the workpiece, the first groove segment or feature formedin the second revolution is displaced by a desired distance in the Zdirection relative to the groove segments or features formed in thefirst revolution. The positions of the groove segments or featuresformed during the second revolution can thus be interleaved between thegroove segments or features formed during the first revolution in knownpositions. Groove segments or features are typically very small, so theeffect has been exaggerated in FIG. 6 for clarity. In an actualcylindrical workpiece, there may be 25,000 to 100,000 groove segmentsformed during a single revolution, for example, so the effect of thehelix angle offset between any two adjacent groove segments would bedifficult to observe As a result, feature overlap lines such as 331 and332, or 431 and 432, may still be noticeable. Another aspect of thepresent invention relates to the minimization or prevention of thevisual significance of these feature overlaps, as described below.

The present invention may advantageously be used to stagger groovessegments or features along a workpiece, or otherwise make the grooves orfeatures appear less repetitive or periodic than those shown in FIGS. 5and 6. For example, grooves may be formed in what may be termed a“four-brick” pattern, as shown in FIG. 7. In this arrangement, groovessegments or features formed during a second revolution of the roll areoffset by ¼ of the length of a single groove segment relative to thefirst revolution, and the groove segments or features formed during athird revolution of the roll are offset by ¼ of the length of a singlegroove segment relative to the second revolution, and so on. In otherwords, the advance per revolution in the Z direction is approximately(and preferably exactly) one-fourth the length of one groove segment.Because FIG. 7 represents very small groove segments formed in a largediameter roll, the helix angle is barely perceptible. A result of thisfour-brick pattern is to make the pattern of the grooves segments orfeatures less visually apparent.

Although “two-brick” and “four-brick” patterns have been described andillustrated specifically, other patterns can be used based on the sameteachings, including odd-numbered brick patterns such as “three-brick,”“five-brick,” and “seven-brick” patterns, for example. These may all becharacterized as “integer” brick patterns, in which the integer isgreater than one, but non-integer brick patterns are also possible (e.g.2.25 brick, 4.5 brick). Different brick patterns may be desirable forvarious end uses, depending on the importance of optical effects.

In the Figures described above, groove segments may be shown as discreteor independent of other grooves, except where at their respective endsthey may overlap with a previous or subsequent groove as in FIG. 5. Anadditional aspect of the present invention is the ability to spaceapart, or abut, or overlap groove segments or other features accordingto a predetermined pattern. If grooves segments on a workpiece arespaced apart from each other, land areas provided between the groovesmay provide certain optical or other advantages in a resulting film,sheeting, or other article made on that workpiece. Groove segments mayabut other groove segments, in the sense that there is essentially noland area between adjacent groove segments, but the groove segments donot interrupt or interfere with the shape or symmetry of adjacent groovesegments. Groove segments may also overlap successive features or groovesegments, so that instead of a regular arrangement of features such asthose shown in FIGS. 5 through 7, an arrangement of features with feweroptically perceptible patterns is provided, as shown in FIG. 8. In thatFigure, successive groove segments are still formed around the perimeterof the roll, for example, but later groove segments overlap earliergroove segments so that the latter no longer appears to be a perfect,whole groove segment of the type shown in FIGS. 5 through 7. Dependingon the location and extent of the overlap, the features cut into theworkpiece can appear to be almost random to an observer, and yet canactually be part of a predetermined pattern. This groove segment-overlapfeature can be used in conjunction with the various “brick” patternsdescribed above.

In another aspect of the present invention, uniform patterns of groovesegments or features formed in a workpiece, whether offset by a helixangle or not, can be measured to determine their regularity orperiodicity. This aspect of the invention involves measuring the grooveor feature depth of successive groove segments along an imaginary lineparallel to the helix angle (or perpendicular to the longitudinal axisof the groove segments if there is no helix angle). For example, thetool in FIG. 3 includes groove segments without a helix angle, and ifthe depth of those grooves were plotted on a bar chart, it would appearas the mono-modal groove depth distribution shown in FIG. 3 a. Thegroove depth of the segment of the tool surface shown in FIG. 5, whichalso has no helix angle, would either be mono-modal (if the imaginaryline bisected the groove segments ¼ of the distance in from the end ofeach segment) or bi-modal (if the imaginary line bisected one groovesegment where it is wider and an adjacent groove segment where it isnarrower. This is shown in FIGS. 5 a and 5 b. A groove depthdistribution for the pattern shown in FIG. 6, measured along a lineparallel to the helix angle, would show the same results as for thepattern shown in FIG. 5, because each is a “two-brick” pattern.

In contrast to the mono-modal or bi-modal groove depth distributionsdescribed with respect to FIGS. 5 and 6, the groove depth distributionsfor the patterns shown in FIGS. 7 and 8 would each be multi-modal,meaning that more than two groove depths would be represented whenmeasured according to the method set forth above. A theoreticalmulti-modal groove depth distribution is illustrated in FIG. 7 a. Thenumber of modes would depend on factors including the degree of overlapbetween adjacent groove segments or features, and where the line alongwhich the groove depths are measured is positioned, among other factors.It is believed that tools displaying multi-modal groove-depthdistribution patterns appear less regular, or more random, to anobserver than do tools displaying mono- or bi-modal groove-depthdistribution patterns, which is another aspect of the present invention.This is believed to be because the areas where groove segments intersectare not all regularly aligned. Similarly, films, sheeting, or otherarticles produced using tools having multi-modal groove-depthdistributions are also believed to appear less regular, or more random,to an observer or user of those articles. Finally, multi-modalgroove-depth distributions may be regular (resulting from an orderedpattern of grooves, as shown in FIGS. 7 and 8, or random (irregular).Tools and articles made using tools having regular multi-modalgroove-depth distributions are an additional aspect of the presentinvention.

In a preferred embodiment of the present invention, the rotation of theworkpiece, the rotation of the fly-cutting head, and the z-axis movementof the fly-cutting head operate in a relatively steady state during theentire process of cutting features into a workpiece. This is preferredbecause it minimizes the time spent stopping, starting, or repositioningthe fly-cutting head or the workpiece, or awaiting the return of one orboth to a steady operating state after a change. It may also help tominimize errors that may occur due to an interruption in the fly-cuttingoperation. One way to achieve this steady-state operating mode is toprogram the controller to run the fly-cutting head and the workpiece atrelatively constant velocities, and to provide for a predeterminedZ-axis advance for each revolution of the roll, so that successivegroove segments (for example) may be formed around the roll on acontinuous and predetermined basis from one end of the roll to the otherend of the roll.

Although the preceding discussion has typically mentioned movement in asingle direction along the Z axis, from an end of a workpiece at whichcutting begins toward the opposite end of a workpiece, the fly-cuttinghead could be programmed to move forward and backward along the Z axisto cut grooves into a workpiece at different successive Z-axispositions, if desired. Also, if a less regular groove pattern weredesired, random differences in the groove positions along the Z axiscould be introduced (referred to as Z-axis noise), as could randomdifferences in the angular position of the workpiece.

FIGS. 9 and 10 illustrate articles made using tools of the typedescribed above. In particular, the articles of FIGS. 9 and 10 may bemicrostructured polymeric films, or film surfaces, that have certainoptically useful properties. The article shown in FIG. 9 exhibits afour-brick pattern, and a multi-modal groove depth distribution, and thearticle shown in FIG. 10 exhibits a two-brick pattern of the typedescribed previously. The structures themselves result from adjacentgroove segments cut into a workpiece, in which the segments overlap atleast at their ends.

Various aspects of the present invention are described as though nofeatures had previously been formed in a workpiece, but the presentinvention may be used to modify, supplement, or complement features thathave been previously been formed in a workpiece. The features may havebeen formed by other milling, turning, or fly-cutting operations, or anyother surface formation or deformation methods now known or laterdeveloped. For example, workpieces are sometimes formed with very smallpyramids on their surfaces, which can facilitate the formation ofpolymeric sheeting with the inverse of those pyramids—cube corners—thatcan reflect incident light. Those pyramids may be formed by threesuccessive passes of a fly-cutting device, any one or more of which mayinclude aspects of the present invention. It may also be useful toperform additional cutting, milling, or other processes to remove ordeform material, or refine surface features, following the fly-cuttingoperations described herein.

The present invention provides a potential solution to an additionalproblem that is frequently encountered in cutting cylindrical tools. Inconventional tool-cutting operations, a cutting element cuts a longgroove into a cylindrical workpiece parallel to the Z axis, theworkpiece or the tool is indexed, and the cutting element cuts a secondlong groove parallel to the first, and so on. In a single revolution ofthe workpiece, the entire surface can be provided with grooves, with thefinal groove being adjacent to the first groove. However, when thecutting element formed the first groove, the cutting element wasrelatively sharp, as shown in FIG. 11, but when the cutting elementformed the final groove, the cutting element was dull, or at least lesssharp, as shown in FIG. 12. FIGS. 11 and 12 are illustrations of acutting element cutting a workpiece as shown in FIG. 2. The contrastbetween the first, sharp groove or other feature and the last, dullgroove or other feature, may create a virtual seam on the workpiece.This effect is shown in FIG. 13, which is a partial or sectionalcut-away view of a portion of a tool cut in accordance with the priorart. At the point where the “sharp” groove cut by a sharp tool isadjacent a final, “dull” groove, a virtual seam results (shown at “VS”in FIG. 13), which will produce a corresponding virtual seam on or in afilm, sheeting, or other article made on that workpiece. The interfacebetween a sharp groove and a less sharp or dull groove is referred to asa “virtual seam” because the seam is an optical one caused by thepresence of different features on each side of a line, not a physicalsplicing of two pieces of material (such as metal tooling or polymericsheeting) together. If the desired final size of the piece of sheetingmade on the tool is less than the circumference of the cylindrical tool,it is possible to trim off the virtual seam, but this produces scrapsheeting, perhaps in considerable quantities. If the size of the finalpiece of sheeting required is greater than the circumference of thetool, then there may be no effective way to avoid using sheeting with avirtual seam.

This problem can be addressed using certain aspects of the presentinvention. If groove segments are formed around the perimeter of theroll, and if successive groove segments formed during second andsubsequent passes of the fly-cutting head are aligned with previousgroove segments, a roll having the equivalent oflongitudinally-extending continuous grooves can be produced. Thismethod, however, creates a tool in which the portions of the grooves atone end of a roll are sharp, and the portions of the grooves at theother end of that roll are less sharp, or dull. More importantly, thereis no point on such a tooling where a sharp groove and a dull groove arenext to each other, and as shown in FIG. 14, no virtual seam is presenton the tool. Also, any resulting sheeting, film, or article producedusing the tool will not include a virtual seam, which is an advantage ofthe present invention. The extent to which a cutting element exhibitswear during use may be characterized by progressively increasingradiuses of curvature in regard to pointed tools, because the pointsbecome rounded, as shown when comparing FIG. 12 to FIG. 11. Althoughonly rounded exterior cutting element ridges or edges are shown in thoseFigures, rounded interior cutting element valleys can also wear andexhibit increasing radiuses of curvature. Wear may also be characterizedby scratches on flat portions, or facets, of a cutting element, or thedeparture from flatness of facets. However, the precise extent of thedifference between a “sharp” tool and a “dull” tool, or between a“sharp” feature or groove and a “dull” feature or groove is unimportantto the present invention, because it is the avoidance of the virtualseam between a relatively sharper groove produced by a relativelysharper tool and a relatively duller groove produced by a relativelyduller tool that is a useful feature of the present invention.Conventional tool-cutting systems are believed to be unable to producethis advantage efficiently.

An additional benefit of the present invention, and specifically ofbeing able to determine the position of a fly-cutting head (and thus itsassociated cutting elements) is that the position or orientation of thecutting element(s) can be changed in a random or predetermined manner toproduce certain desirable effects. For example, the position of acutting element may be controlled by a controller so that it changesduring the time that the cutting element is forming a feature in aworkpiece, resulting in a feature having a predetermined shape,position, or both. This is achieved, in one embodiment of the invention,but changing the position or orientation or both of a cutting element(either alone or together with a cartridge or carrier) using anactuator.

The actuator may be any device that effectuates a change in position ororientation of a cutting element, and may be a component of a fast toolservo (FTS). A fast tool servo typically includes a solid statepiezoelectric (“PZT”) device, referred to as a PZT stack, which canrapidly adjust the position of a cutting tool attached to the PZT stack.PZT stacks are available that have sub-nanometer positioning resolution,and they react very quickly and exhibit essentially no wear aftermillions or even billions of cycles. Actuators, such as those includedin fast tool servos, may be used in closed loop operations, togetherwith a position sensor that enables the actuator to adjust forpositioning discrepancies, or in open loop operations with no positionsensor. An actuator receives signals from the controller, and therebycontrols the manner in which cutting element creates features such asgroove segments or grooves in the workpiece. The actuator is preferablyremovably connected to the fly-cutting head either directly, orindirectly via a cartridge or carrier. Although the actuator may extendthe cutting element along the X axis only, actuators may be providedthat would move a cutting element along any axis, or (rotationally)around any axis.

The actuator may receive more than one signal or type of signal, throughone or more wires, optical fibers, or other signal transmission devices.For example, the actuator may receive AC or DC power, to create themotive force necessary to change the position or orientation of the toolholder. The actuator may also receive a drive signal, which may beproportional to the change in position or orientation to be effectuatedby the actuator. The actuator may receive a reference signal, such as azero-voltage signal, that permits or causes it to return to its initialstate, position, or orientation. Finally, the actuator or associatedhardware may transmit feedback signals that provide information aboutthe position or relative position of a tool holder or cutting element,for example, so that subsequent changes in the position or orientationof the tool holder or cutting element can be adapted appropriately.Signals of the type described, or other signals, can be transmittedthrough dedicated wires or optical fibers, or where appropriate they maybe multiplexed along a single wire or optical fiber. The transmission ofpower and of the signals described herein, or any other necessary oruseful signals, may also require the use of a slip ring or othermechanism for transferring signals from a stationary component to arotating component, as is known in the art. One slip ring that mayuseful is available from Fabricast, Inc. of South El Monte, California,under the product number designation 09014. Other components fortransferring power or signals, or both, include mercury wetted sliprings, fiber-optic rotary joints (FORJs), and contactless magnetic sliprings.

Although a cutting element cartridge or carrier may be useful in certainembodiments of the invention to facilitate the replacement and accuratepositioning of the cutting element, it may be possible to mount acutting element directly on an actuator without such a carrier. Thecutting element may be secured to the cutting element carrier by anadhesive, brazing, soldering, or in other ways, or directly to anactuator.

Articles, such as polymeric films and sheeting, made on tools accordingto the present invention, or made according to the present invention,may be useful in displays, such as monitors or televisions, or asreflective or retroreflective sheeting of the type used on road signs,or for other purposes. In another embodiment of the present invention,the structure of the tool (a master tool) can be transferred on othermedia, such as to a belt or web of polymeric material, by a cast andcure process to form a production tool. This production tool is thenused to make a microreplicated article of the type described herein.This results in an article having a surface that corresponds to thesurface of the master tool. Other methods, such as electroforming, canalso be used to copy the master tool. That copy, which may be referredto as an intermediate tool, can then be used to produce themicroreplicated article.

In other embodiments of the invention, the cutting elements need notproject radially from the fly-cutting head as with conventionalfly-cutting heads. Instead or in addition, the cutting elements couldextend parallel or generally parallel to the axis of rotation of thefly-cutting head. The cutting elements can be controlled by actuators inthe manner described above, and used in an operation referred to as“face-cutting” or “face fly-cutting” to cut certain patterns or featuresinto the surface of a workpiece. In this embodiment, the cuttingelements are essentially in continuous contact with the workpiece, notintermittent contact as is normally the case with conventionalfly-cutting.

Microreplicated structures such as sheeting of the type described abovehave been used for retroreflective road signs and license plates forvehicles, for displays such as the displays in portable computers tocontrol the emission of light toward the viewer, other optical films,abrasive or friction-control films, adhesive films, mechanical fastenershaving self-mating profiles (as disclosed in U.S. Pat. No. 5,360,270,for example), or any molded or extruded parts having microreplicatedfeatures of relatively small dimensions, such as dimensions less thanapproximately 1000 microns.

The present invention has now been described with respect to severalembodiments thereof, but persons of skill in the field will understandthat modifications of the invention may be made without departing fromthe spirit and scope of the invention. For example, structures describedas grooves may be features with other characteristics, workpiecesdescribed as cylindrical may have other shapes instead, and variouscomponents of the system may be assembled in a different manner toachieve the same results. Accordingly, the invention shall be limitednot by the foregoing disclosure, but by the following claims, and theirequivalents.

1. A polymeric article formed using a tool and having features formed bythe tool, wherein the tool comprises a cylindrical tool comprising aplurality of groove segments individually formed around the perimeter ofthe tool, the groove segments being aligned with other groove segmentsto form generally uniform longitudinally-extending grooves in the tool.2. A polymeric article formed using a tool and having features formed bythe tool, wherein the tool comprises a cylindrical tool having groovesegments formed therein, wherein the groove segments have a beginningand an end, and the groove segments are arranged according to an integerbrick pattern, wherein the integer is greater than one.
 3. A polymericarticle formed using a tool and having features formed by the tool,wherein the tool comprises a cylindrical tool having groove segmentsformed therein, wherein the groove segments have a beginning and an end,and successive groove segments are offset with respect to previousgroove segments by a helix angle.
 4. A polymeric article formed using atool and having features formed by the tool, wherein the tool comprisesa cylindrical tool comprising a plurality of groove segments, whereinthe groove segments are individually formed in positions relative toeach other, and wherein the groove depth distribution of successiveadjacent grooves, measured along a line that is parallel to any helixangle associated with the groove segments, is multi-modal.
 5. Apolymeric article, comprising: a series of features formed in thearticle, wherein the series of features have a beginning and an end, andthe features are arranged according to an integer brick pattern, whereinthe integer is greater than one.
 6. The polymeric article of claim 5,wherein the article comprises an optical film.
 7. The polymeric articleof claim 5, wherein the article comprises a friction-control film. 8.The polymeric article of claim 5, wherein the article comprises anadhesive film.
 9. The polymeric article of claim 5, wherein the articlecomprises mechanical fasteners having self-mating profiles.
 10. Apolymeric article having features formed in the article, comprising: afirst substantially linear series of partially overlapping firstindividual features; a second substantially linear series of partiallyoverlapping second individual features; and a third substantially linearseries of partially overlapping third individual features, wherein thefirst, second, and third series of the first, second, and thirdindividual features collectively form cube corners.
 11. The polymericarticle of claim 10, wherein the first, second, and third individualfeatures comprise pyramids.